# Rene Descartes - Mathematician

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Renй Descartes:

“Father of Modern Mathematics"

1596-1650

December 13, 2004

Renй Descartes was born in La Haye, Touraine (France) in March of 1596 and died at Stockholm on February 11, 1650. Renй, the second of a family of two sons and one daughter, was sent to the Jesuit School at La Flкche at the early age of eight. Since he was of poor health he was permitted to lie in bed till late in the mornings, a custom which he always followed. When Pascal visited in 1647 he told him that the only way to do good work in mathematics and to preserve his health was never to allow anyone to make him get up in the morning before he felt like it

On leaving school in 1612 Descartes went to Paris to be introduced to the world of fashion. Through the medium of the Jesuits, he met Mydorge, and renewed his childhood friendship with Mersenne. Together they devoted two years, from 1615 1617, to the study of mathematics. During that time a man of position usually entered either the army or the church and so in 1617 Descartes joined the army of Prince Maurice of Orange, then at Breda. Walking through the streets one day in Breda he noticed a placard in Dutch which made him quite curious. He asked a stranger to translate it into either French or Latin. The stranger was Isaac Beeckman, the head of the Dutch College at Dort. He told Descartes he would do so only if he would answer it for him. The placard was a challenge to the world to solve a certain geometrical problem. Descartes worked it out within a few hours, and a close friendship had formed between the two.This unexpected test of his mathematical attainments made the unpleasant life of the army distasteful to him, but because of family influence and tradition he remained a soldier. He was persuaded at the commencement of the Thirty Years' War he was persuaded to volunteer under Count de Bucquoy in the Bavarian army. He continued all this time however, to occupy his leisure with mathematical studies. He would date the first ideas of his philosophy and of his analytical geometry according to three dreams which he experienced on the night of November 10, 1619, at Neuberg. He regarded this day as one which determined his whole future.

Descartes resigned his commission in the spring of 1621, and spent the next five years traveling and studying mathematics. He settled in Paris 1626 and during the first few years there spent his time constructing optical instruments. Although he took time off for these pursuits he was still convinced that someday find in philosophy the theory of the universe.

In 1628, the founder of the Oratorians, Cardinal de Berulle, met Descartes, and was very impressed. He urged him to devote his life to the examination of truth. Descartes agreed, at the height of his power moved to Holland. He lived there for twenty years, giving up all his time to philosophy and mathematics. Descartes spent the first four years, from 1629 to 1633, writing Le Monde, an attempt to give a physical theory of the universe. Realizing that its publication was likely to create hostility in the church, he abandoned it. He then devoted himself to composing a treatise on universal science; “Discours de la mйthode pour bien conduire sa raison et chercher la vйritй dans les sciences,” and he accompanied it with three appendices entitled La Dioptrique, Les Mйtйores, and La Gйomйtrie. In 1641 he wrote “Meditationes,” in which he explained at some length his views on philosophy. In 1644 he issued the Principia Philosophiae, which was devoted to physical science, especially the laws of motion and the theory of vortices. In 1647 he received a pension from the French court for his discoveries. Descartes went to Sweden on the invitation of the Queen in 1649, and died only a few months later of inflammation of the lungs.

Descartes wore many hats: he was a soldier, a teacher, a mathematician, and a philosopher. One could say that modern mathematics actually began with the work of Descartes. His invention of coordinate geometry paved the way for advances in mathematics. Descartes invented what we now call Cartesian coordinates, a system where we can graph mathematical functions in two-or

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